Holistic Twig Joins on Indexed XML Documents 6

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Holistic Twig Joins on Indexed XML Documents 6

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Title: Holistic Twig Joins on Indexed XML Documents 6

1
Holistic Twig Joins on Indexed XML Documents 6

by Haifeng Jiang, Wei Wang, Hongjun Lu, and
Jeffrey Xu Yu
Presented by Teddy Yap, Jr.
CS267, April 14, 2004

2
Outline of Presentation

Looking Back
Introduction and Motivation
Background and Related Work
The Generic Twig Join Algorithm
The TSGeneric Algorithm
A Performance Study
Conclusions

3
Outline of Presentation

Looking Back
Introduction and Motivation
Background and Related Work
The Generic Twig Join Algorithm
The TSGeneric Algorithm
A Performance Study
Conclusions

4
Looking Back

1 S. Al-Khalifa, H. V. Jagadish, N. Koudas, J.
M. Patel, D. Srivastava, and Y. Wu, Structural
Joins A Primitive for Efficient XML Query
Pattern Matching. Proc. ICDE Conf. 2002.

XML query pattern
Results
XML Database
5
Looking Back (2)
6
Looking Back (3)
7
Looking Back (4)
8
Looking Back (5)
9
Looking Back (6)
10
Looking Back (7)
11
Looking Back (8)

3 S.-Y. Chien, Z. Vagena, D. Zhang, V. J.
Tsotras, and C. Zaniolo, Efficient Structural
Joins on Indexed XML Documents. Proc. of VLDB
Conf., 2002.

12
Looking Back (9)
13
Looking Back (10)
14
Looking Back (11)

5 Haifeng Jiang, Hongjun Lu, Wei Wang, and Beng
Chin Ooi, XR-Tree Indexing XML Data for
Efficient Structural Joins. Proc. of ICDE
Conf., 2003.

15
Looking Back (12)
16
Looking Back (13)

2 Nicolas Bruno, Nick Koudas, and Divesh
Srivastava, Holistic Twig Joins Optimal XML
Pattern Matching. Proc. of ACM SIGMOD Conf.
2002.

17
Looking Back (14)
18
Outline of Presentation

Looking Back
Introduction and Motivation
Background and Related Work
The Generic Twig Join Algorithm
The TSGeneric Algorithm
A Performance Study
Conclusions

19
Introduction and Motivation

XML emerging as a de facto standard for
information exchange over the Internet
XML documents modeled as ordered trees
XML queries specify patterns of selection
predicates on multiple elements having some
structural relationships (parent-child,
ancestor-descendant)

20
Introduction and Motivation (2)

Sample XML query
//section//paragraphfigure AND table

21
Introduction and Motivation (3)

Locating all occurrences of a twig pattern is a
core operation in XML query processing.

Decomposition Approach
section
section
paragraph
paragraph
paragraph
paragraph
figure
table
figure
table
22
Introduction and Motivation (4)

Disadvantage of the decomposition approach
Intermediate result sizes can get very large,
even when the input and the final result sizes
are much more manageable.
Solution Holistic twig join approach for
matching XML query twig patterns 2

23
Introduction and Motivation (5)

Motivation Although the proposed holistic twig
join algorithm 2 has been proven to be I/O and
CPU optimal in terms of input and output sizes
for twigs with only ancestor-descendant edges,
the potential benefit of skipping elements that
do not participate in the final twig match by
using available indices (e.g. B-trees, XR-trees)
is not fully explored.

24
Introduction and Motivation (6)

In a nutshell
A generic algorithm TSGeneric which can utilize
available indices (e.g. XR-trees 5) on element
sets to quickly locate the first match for a sub
twig pattern thus skipping those edges that do
not comply with the desired structural
relationship (e.g. ancestor-descendant
relationship) with a structural join like
algorithm.

25
Introduction and Motivation (7)

Main issue
Which edge to choose first so that more elements
without matches can be skipped?
Three edge-picking heuristics
Top-down
bottom-up
Statistics-based

26
Outline of Presentation

Looking Back
Introduction and Motivation
Background and Related Work
The Generic Twig Join Algorithm
The TSGeneric Algorithm
A Performance Study
Conclusions

27
Background and Related Work

Data model and numbering scheme

28
Background and Related Work (2)

Corollary 1
Given two elements ei and ej, if ei.start lt
ej.start and ei is not an ancestor of ej, then ei
will not be an ancestor of any element ex with
ex.start gt ej.start.

ei
ej
29
Background and Related Work (3)

Structural Joins
A structural join is to find all occurrences of a
given structural relationship between two sets of
elements.
Algorithms
MPMGJN 8
? ?/ ?A-Join 7
Stack-Tree-Desc/Anc 1
Index-based approaches 3, 4, 5

30
Background and Related Work (4)

Twig Pattern Matching
Given a query twig pattern Q and an XML database
D, a match of Q in D is identified by a mapping
from nodes in Q to nodes in D, s.t.
query node predicates are satisfied by the
corresponding database nodes
the structural relationships between query nodes
are satisfied by the corresponding database nodes.

Answer (d1, d2, , dn)
31
Background and Related Work (5)

Related Work
2 Nicolas Bruno, Nick Koudas, and Divesh
Srivastava, Holistic Twig Joins Optimal XML
Pattern Matching. Proc. of ACM SIGMOD Conf.
2002.

32
Outline of Presentation

Looking Back
Introduction and Motivation
Background and Related Work
The Generic Twig Join Algorithm
The TSGeneric Algorithm
A Performance Study
Conclusions

33
The Generic Twig Join Algorithm

Preliminaries
isRoot(q)
isLeaf(q)
children(q)
parent(q)
subtreeNodes(q)

34
The Generic Twig Join Algorithm (2)

Assumptions
Each node in the query tree has an associated
data stream.
Every element in the data stream is already
encoded in the following region format (start,
end, level) and sorted on the start attribute.
2 types of data structures for every node q ? T
cursor (Cq) and stack (Sq).

35
The Generic Twig Join Algorithm (3)

Illustration

36
The Generic Twig Join Algorithm (4)

Sample XML Document

37
The Generic Twig Join Algorithm (5)
Ca
a
a1, a2, a3, a4, a5, a6, a7
Cb
Sa
b1, b2, b3, b4, b5
b
Sc
Sb
Cc
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
c
38
The Generic Twig Join Algorithm (6)

Notation
The cursor Cq is simply a pointer to some element
in the data stream for node q.
Methods and Attributes
Cq -gt advance( ) move to next element
Cq -gt start
Cq -gt end
Cq -gt level

39
The Generic Twig Join Algorithm (7)

Initial Configuration
All stacks are empty.
All cursors point to the first element of the
corresponding data stream.

40
The Generic Twig Join Algorithm (8)

Stack Sq
Used to cache some elements before the cursor Cq
Elements are strictly nested from bottom to top.
Each element e in Sq has a pointer to the lowest
ancestor in Sparent(q).
Cached elements represent partial results than
can be extended further.

41
The Generic Twig Join Algorithm (9)

Illustration

42
The Generic Twig Join Algorithm (10)

Definition (Solution Extension)
We say that a node q has a solution extension if
there is a solution for the sub query rooted at q
composed entirely of the cursor elements of the
query nodes in the sub query.

43
The Generic Twig Join Algorithm (11)

Implication
If node q has a solution extension, since Cq is
the ancestor of all cursor elements in the sub
query tree nodes, Cq -gt start is smaller than all
cursor start values of query nodes in the subtree
q.

44
The Generic Twig Join Algorithm (12)

getNext(q)

45
The Generic Twig Join Algorithm (13)

getNext(q)
Returns a query node qx in the subtree q
satisfying all the following
qx has a solution extension.
if qx has siblings, Cqx -gt start lt Cqs -gt start
for all sibling qs of qx.
If qx ? q, Cparent(qx) -gt start gt Cqx -gt start.

46
The Generic Twig Join Algorithm (14)

getNext(q)

If q is a leaf, return q.
If q is not a leaf, determine if the children of
q has solution extension rooted at them,
else return descendant of q with
solution extension.
Determine descendant of q with minimum and
maximum start attribute. Advance cursor of q so
so that Cq -gt end gt Cnmax -gt start. If Cq -gt
start lt Cnmin -gt start return node q, else return
descendant nmin of q with minimum start attribute.
Corollary 1
47
The Generic Twig Join Algorithm (15)

getNext(q) (Examples)

48
The Generic Twig Join Algorithm (16)

getNext(q) (Examples)

getNext(root) ?
a
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b
b3
c1
c2
c4
c8
c11
c
c3
c5
c6
c7
c9
c10
c12
Data Streams and Cursors
Ca
Cb
Cc
a1, a2, a3, a4, a5, a6, a7
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
49
The Generic Twig Join Algorithm (16)

getNext(q) (Examples)

getNext(root) c
a
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b
b3
c1
c2
c4
c8
c11
c
c3
c5
c6
c7
c9
c10
c12
Data Streams and Cursors
Ca
Cb
Cc
a1, a2, a3, a4, a5, a6, a7
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
50
The Generic Twig Join Algorithm (17)

getNext(q) (Examples)

getNext(q) (Examples)

getNext(q) (Examples)

getNext(q) (Examples)

getNext(q) (Examples)

getNext(q) (Examples)

getNext(q) (Examples)

getNext(root) ?
a
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b
b3
c1
c2
c4
c8
c11
c
c3
c5
c6
c7
c9
c10
c12
Data Streams and Cursors
Cb
Cc
a1, a2, a3, a4, a5, a6, a7
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
57
The Generic Twig Join Algorithm (20)

getNext(q) (Examples)

getNext(q) (Examples)

getNext(q) (Examples)

getNext(q) (Examples)

getNext(root) b
a
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b
b3
c1
c2
c4
c8
c11
c
c3
c5
c6
c7
c9
c10
c12
Data Streams and Cursors
Ca
Cb
Cc
a1, a2, a3, a4, a5, a6, a7
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
61
The Generic Twig Join Algorithm (21)

TSGeneric(root)

62
The Generic Twig Join Algorithm (22)

TSGeneric(root)

Get node q with solution extension.
63
The Generic Twig Join Algorithm (22)

TSGeneric(root)

If node q is not a root node, pop all
elements that are not ancestor of Cq from its
parents stack.
64
The Generic Twig Join Algorithm (22)

TSGeneric(root)

If node q is a root node or its parent stack is
not empty, pop all elements from Sq that are not
ancestors of Cq. If node q is not a leaf, push
the pair (Cq, top(Sparent(q))) onto stack Sq
where top(Sparent(q)) returns a pointer to the
top element in Sparent(q). Otherwise, output
path solutions.
65
The Generic Twig Join Algorithm (22)

TSGeneric(root)

Advance cursor Cq so it points to the
next element in the data stream for node q.
66
The Generic Twig Join Algorithm (22)

TSGeneric(root)

Merge all path solutions.
67
The Generic Twig Join Algorithm (23)

TSGeneric (Examples)

getNext(root) ?
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
68
The Generic Twig Join Algorithm (23)

TSGeneric (Examples)

getNext(root) b
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
69
The Generic Twig Join Algorithm (24)

TSGeneric (Examples)

getNext(root) ?
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
70
The Generic Twig Join Algorithm (24)

TSGeneric (Examples)

getNext(root) c
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
71
The Generic Twig Join Algorithm (25)

TSGeneric (Examples)

TSGeneric (Examples)

getNext(root) b
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
73
The Generic Twig Join Algorithm (26)

TSGeneric (Examples)

TSGeneric (Examples)

TSGeneric (Examples)

TSGeneric (Examples)

TSGeneric (Examples)

TSGeneric (Examples)

TSGeneric (Examples)

getNext(root) ?
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
80
The Generic Twig Join Algorithm (29)

TSGeneric (Examples)

getNext(root) c
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
81
The Generic Twig Join Algorithm (30)

TSGeneric (Examples)

TSGeneric (Examples)

TSGeneric (Examples)

getNext(root) a
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
84
The Generic Twig Join Algorithm (31)

TSGeneric (Examples)

getNext(root) ?
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
a7
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
85
The Generic Twig Join Algorithm (31)

TSGeneric (Examples)

getNext(root) b
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
a7
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
86
The Generic Twig Join Algorithm (32)

TSGeneric (Examples)

getNext(root) ?
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
a7
b4
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
87
The Generic Twig Join Algorithm (32)
Output (a7, b4, c9)

TSGeneric (Examples)

getNext(root) c
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
a7
b4
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
88
The Generic Twig Join Algorithm (33)

TSGeneric (Examples)

getNext(root) ?
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
a7
b4
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
89
The Generic Twig Join Algorithm (33)
Output (a7, b4, c10)

TSGeneric (Examples)

TSGeneric (Examples)

TSGeneric (Examples)

getNext(root) c
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
a7
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
92
The Generic Twig Join Algorithm (35)

TSGeneric (Examples)

TSGeneric (Examples)

TSGeneric (Examples)

getNext(root) ?
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
a7
b5
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
95
The Generic Twig Join Algorithm (36)
Output (a7, b5, c12)

TSGeneric (Examples)

getNext(root) c
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
a7
b5
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
96
The Generic Twig Join Algorithm (37)

TSGeneric (Examples)

a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
a7
b5
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
97
The Generic Twig Join Algorithm (38)

TSGeneric
Can we accelerate twig join processing in
TSGeneric by taking advantage of available
indices?
Answer Sure.

98
The Generic Twig Join Algorithm (39)

Two New Methods
Cq -gt fwdBeyond(Cp) forwards Cq to the first
element e, such that e.start gt Cp -gt start.
Cq -gt fwdToAncestorOf(Cp) forwards the cursor to
the first ancestor of Cp and returns TRUE. If no
such ancestor exists, it stops at the first
element e, such that e.start gt Cp -gt start, and
returns FALSE.

99
The Generic Twig Join Algorithm (40)

getNextCursor(q)

100
The Generic Twig Join Algorithm (41)

getNextCursor(q)

If we find a common ancestor for all
child cursors, we return q otherwise, we
return the child node with minimum start value.
101
The Generic Twig Join Algorithm (42)

getNextCursor(q) (Ex.)

getNextCursor(root) ?
a
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b
b3
c1
c2
c4
c8
c11
c
c3
c5
c6
c7
c9
c10
c12
Data Streams and Cursors
Ca
Cb
Cc
a1, a2, a3, a4, a5, a6, a7
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
102
The Generic Twig Join Algorithm (42)

getNextCursor(q) (Ex.)

getNextCursor(root) c
a
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b
b3
c1
c2
c4
c8
c11
c
c3
c5
c6
c7
c9
c10
c12
Data Streams and Cursors
Ca
Cb
Cc
a1, a2, a3, a4, a5, a6, a7
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
103
The Generic Twig Join Algorithm (43)

getNextCursor(q) (Ex.)

getNextCursor(q) (Ex.)

getNextCursor(q) (Ex.)

getNextCursor(q) (Ex.)

getNextCursor(q) (Ex.)

getNextCursor(q) (Ex.)

getNextCursor(q) (Ex.)

getNextCursor(root) ?
a
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b
b3
c1
c2
c4
c8
c11
c
c3
c5
c6
c7
c9
c10
c12
Data Streams and Cursors
Cb
Cc
a1, a2, a3, a4, a5, a6, a7
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
110
The Generic Twig Join Algorithm (46)

getNextCursor(q) (Ex.)

getNextCursor(root) b
a
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b
b3
c1
c2
c4
c8
c11
c
c3
c5
c6
c7
c9
c10
c12
Data Streams and Cursors
Cb
Cc
a1, a2, a3, a4, a5, a6, a7
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
111
The Generic Twig Join Algorithm (47)

getNextCursor(q) (Ex.)

getNextCursor(q) (Ex.)

getNextCursor(root) c
a
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b
b3
c1
c2
c4
c8
c11
c
c3
c5
c6
c7
c9
c10
c12
Data Streams and Cursors
Cb
Cc
a1, a2, a3, a4, a5, a6, a7
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
113
The Generic Twig Join Algorithm (48)

getNextCursor(q) (Ex.)

getNextCursor(root) ?
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
114
The Generic Twig Join Algorithm (48)

getNextCursor(q) (Ex.)

getNextCursor(root) b
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
115
The Generic Twig Join Algorithm (49)

getNextCursor(q) (Ex.)

getNextCursor(q) (Ex.)

getNextCursor(q) (Ex.)

getNextCursor(q) (Ex.)

getNextCursor(root) c
a1
a5
a7
a2
a4
a6
a3
b1
b2
b4
b5
b3
c1
c2
c4
c8
c11
c3
c5
c6
c7
c9
c10
c12
Ca
a1, a2, a3, a4, a5, a6, a7
Cb
Cc
b1, b2, b3, b4, b5
c1, c2, c3, c4, c5, c6, c7, c8, c9, c10, c11, c12
Sc
Sb
Sa
119
The Generic Twig Join Algorithm (51)